Theorems · Theorem · commutative algebra

MvPowerSeries.weightedOrder_add_of_weightedOrder_ne

∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f g : MvPowerSeries σ R},
  MvPowerSeries.weightedOrder w f ≠ MvPowerSeries.weightedOrder w g →
    MvPowerSeries.weightedOrder w (f + g) = min (MvPowerSeries.weightedOrder w f) (MvPowerSeries.weightedOrder w g)

The weightedOrder of the sum of two formal power series is the minimum of their orders if their orders differ.

Defined in: Mathlib.RingTheory.MvPowerSeries.Order
Cited by: 2 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Semiringstatement and proof · cited by 13,802
ENatstatement and proof · cited by 4,985
le_antisymmproof · cited by 2,068
le_rflproof · cited by 1,558
add_commproof · cited by 1,535
le_of_ltproof · cited by 1,175
MvPowerSeriesstatement and proof · cited by 659
le_of_not_gtproof · cited by 430
inf_commproof · cited by 139
LE.le.lt_of_ne'proof · cited by 41
MvPowerSeries.weightedOrderstatement and proof · cited by 37
MvPowerSeries.min_weightedOrder_le_addproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

MvPowerSeries.weightedOrder_negproof · cited by 1
MvPowerSeries.order_add_of_order_neproof · cited by 0